Torus knots and links, the subject of belcastro's talk, can be made by wrapping a string around a torus, or a donut. You can think of a torus as the shape you get when you sweep a circle around another circle as in the diagram below.

We can think of the red circle and the pink circle, the circles that wrap through the hole or around the hole, respectively, as the two main "directions" on the torus, analogous to latitude and longitude on a sphere.

A
torus knot
or link is defined by how many times it wraps around the two main directions. A (
p,q
) torus link* wraps
p
times through the center (along the red circle) and
q
times around the hole (along the pink circle). If we use a negative number instead a positive one for
p
or
q
, the description is the same, but the knot or link spirals around the torus in a different direction. For more illustrations of torus knots, check out the
Knot Atlas
.

Any two integers
p
and
q
can define a torus link. If the numbers don't share a common factor, the link only has one piece, so we call it a knot. If they do share a common factor, the link has more than one piece, like this (4,2) torus link. (The number of pieces is the same as the largest common factor that
p
and
q
share.)

Belcastro is both a mathematician and a knitter, and she has become adept at
combining
the two subjects. She uses mathematics to understand and guide her knitting and knitting to visualize complicated mathematical objects. A few years ago, belcastro started knitting tori using contrasting yarn to illustrate torus knots on them.

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The above tweet fairly accurately captures millennials’ current attitude about climate change. It’s easy to retweet a pithy status in support of saving the earth; it’s harder to actually save the earth.

According to an
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, the platform is the result of talks at the World Economic Forum about “how to inspire and accelerate the shift toward a more sustainable way of life.” It’s dedicated to “altering the course of our collective futures” and repairing “the disconnect between our wishes for the future of the planet and the tools we have to get there.”

While today’s media is “obsessed with fear-mongering tactics” that leave people fearful of and ineffectual towards earth’s imminent self-inflicted demise, writes Carr-Harris, “Collectively will break through that negativity and cynicism to help people learn how they can help. Take meaningful action. Choose to make a difference.”

Collectively CEO Will Gardner told Mashable via email that the site would be editorially independent of the brands backing it.

“Our brand sponsors have signed up to support an editorially independent site. Our policy is to highlight a range of positive and exciting ideas and solutions to sustainable living challenges, from wherever they come in the world,” Gardner said.

“Carr-Harris noted that companies and people need to work together figure out what we can do about climate issues,” writes Abbruzzese, “as long as that means not pointing to the cause of these issues.”

Encryption context can consist of any values that you want. However, because it is not encrypted and because it is logged if CloudTrail logging is turned on, your encryption context should not include sensitive information. We further recommend that your encryption context describe the data being encrypted or decrypted so that you can better understand the CloudTrail log entries produced by AWS KMS. For example, Amazon EBS uses the ID of the encrypted volume as the encryption context for server-side encryption. If you are encrypting a file, you might use part of the file path as encryption context.

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Encryption Context in Grants and Key Policies

In addition to using encryption context to check ciphertext integrity and authenticity, AWS KMS supports authorization by using grants and key policies that incorporate encryption context. Authorization that uses encryption context more tightly controls access to encrypted resources. When you
create a grant
, for example, you can optionally specify a set of constraints that specify an encryption context that unambiguously identifies the resource to which long-term access is being granted. For example, consider encrypted volumes with Amazon EBS and Amazon EC2: When an EBS volume is attached to an EC2 instance, a grant is created that allows only that instance to decrypt only that volume. This is accomplished by encoding the volume ID as the encryption context in the
Constraint
that is passed to the
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API. Without the encryption context in the constraint, the Amazon EC2 instance would obtain access to all volumes encrypted under the customer master key (CMK) rather than a specific volume.